Diffraction by DNA, carbon nanotubes and other helical nanostructures

This review discusses the diffraction patterns of x-rays or electrons scattered by fibres of helical biological molecules and by carbon nanotubes (CNTs) from the unified point of view of the Fourier-Bessel transform of an atomic helix. This paper is intended for scientists who are not professional crystallographers. X-ray fibre diffraction patterns of Pauling's protein a-helix and of Crick and Pauling's protein coiled-coil are revisited. This is followed by a non-technical comparison between the historic x-ray diffraction patterns of the A and B conformations of DNA, which were crucial for the discovery of the double helix. The qualitative analysis of the diffraction images is supported by novel optical simulation experiments designed to pinpoint the gross structural informational content of the patterns. The spectacular helical structure of the tobacco mosaic virus detennined by Rosalind Franklin and co-workers will then be described as an early example of the great power of x-ray crystallography in determining the structure of a large biomolecular edifice. After these mostly historical and didactic case studies, this paper will consider electron diffraction and transmission electron microscopy of CNTs of great current interest, focusing particularly on recent data obtained for single-wall, double-wall and scrolled nanotubes. Several points of convergence between the interpretations of the diffraction patterns of biological helices and CNTs will be emphasized.